1635:
1061:
589:
1630:{\displaystyle {\begin{matrix}1&2&3&4&5\\2&3&4&5&1\\3&4&5&1&2\\4&5&1&2&3\\5&1&2&3&4\end{matrix}}\qquad {\begin{matrix}1&2&3&4&5\\3&4&5&1&2\\5&1&2&3&4\\2&3&4&5&1\\4&5&1&2&3\end{matrix}}\qquad {\begin{matrix}1&2&3&4&5\\5&1&2&3&4\\4&5&1&2&3\\3&4&5&1&2\\2&3&4&5&1\end{matrix}}\qquad {\begin{matrix}1&2&3&4&5\\4&5&1&2&3\\2&3&4&5&1\\5&1&2&3&4\\3&4&5&1&2\end{matrix}}.}
701:
3179:
1050:
8435:
6124:
2836:
183:
195:
755:
3174:{\displaystyle {\begin{matrix}1&2&3&4\\2&1&4&3\\3&4&1&2\\4&3&2&1\\&L_{1}&&\end{matrix}}\qquad \qquad {\begin{matrix}1&2&3&4\\4&3&2&1\\2&1&4&3\\3&4&1&2\\&L_{2}&&\end{matrix}}\qquad \qquad {\begin{matrix}1&2&3&4\\3&4&1&2\\4&3&2&1\\2&1&4&3\\&L_{3}&&\end{matrix}}}
549:
8421:
1045:{\displaystyle {\begin{matrix}1&2&3&4\\2&1&4&3\\3&4&1&2\\4&3&2&1\end{matrix}}\qquad \qquad {\begin{matrix}1&2&3&4\\4&3&2&1\\2&1&4&3\\3&4&1&2\end{matrix}}\qquad \qquad {\begin{matrix}1&2&3&4\\3&4&1&2\\4&3&2&1\\2&1&4&3\end{matrix}}.}
8459:
8447:
327:
of that square. Consider one symbol in a Graeco-Latin square. The positions containing this symbol must all be in different rows and columns, and furthermore the other symbol in these positions must all be distinct. Hence, when viewed as a pair of Latin squares, the positions containing one symbol in
572:
A very curious question, which has exercised for some time the ingenuity of many people, has involved me in the following studies, which seem to open a new field of analysis, in particular the study of combinations. The question revolves around arranging 36 officers to be drawn from 6 different
709:
Extensions of mutually orthogonal Latin squares to the quantum domain have been studied since 2017. In these designs, instead of the uniqueness of symbols, the elements of an array are quantum states that must be orthogonal to each other in rows and columns. In 2021, an Indian-Polish team of
2435:= 10. From the Graeco-Latin square construction, there must be at least two and from the non-existence of a projective plane of order 10, there are fewer than nine. However, no set of three MOLS(10) has ever been found even though many researchers have attempted to discover such a set.
714:) found an array of quantum states that provides an example of mutually orthogonal quantum Latin squares of size 6; or, equivalently, an arrangement of 36 officers that are entangled. This setup solves a generalization of the 36 Euler's officers problem, as well as provides a new
704:
A quantum solution to a classically impossible problem. If the chess pieces are quantum states in a superposition, then a pair of orthogonal quantum Latin squares of size 6 exists. The relative sizes of chess pieces denote the contribution of the corresponding quantum
379:
in 1725. The problem was to take all aces, kings, queens and jacks from a standard deck of cards, and arrange them in a 4 x 4 grid such that each row and each column contained all four suits as well as one of each face value. This problem has several solutions.
58:, which ensures that independent variables are truly independent with no hidden confounding correlations. "Orthogonal" is thus synonymous with "independent" in that knowing one variable's value gives no further information about another variable's likely value.
1743:
In the examples of MOLS given so far, the same alphabet (symbol set) has been used for each square, but this is not necessary as the Graeco-Latin squares show. In fact, totally different symbol sets can be used for each square of the set of MOLS. For example,
539:
For each of the two solutions, 24×24 = 576 solutions can be derived by permuting the four suits and the four face values, independently. No permutation will convert the two solutions into each other, because suits and face values are different.
1973:, meaning that the first row of every square is identical and normally put in some natural order, and one square has its first column also in this order. The MOLS(4) and MOLS(5) examples at the start of this section have been put in standard form.
4920:
Rather, Suhail Ahmad; Burchardt, Adam; Bruzda, Wojciech; Rajchel-MieldzioÄ, Grzegorz; Lakshminarayan, Arul; Ć»yczkowski, Karol (2022), "Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem",
2385:
2244:
2086:
is a prime or prime power, so projective planes of such orders exist. Finite projective planes with an order different from these, and thus complete sets of MOLS of such orders, are not known to exist.
3728:
For example, the OA(5,4) in the above section can be used to construct a (5,4)-net (an affine plane of order 4). The points on each line are given by (each row below is a parallel class of lines):
5128:
The term "order" used here for MOLSs, affine planes and projective planes is defined differently in each setting, but these definitions are coordinated so that the numerical value is the same.
2739:
Not all complete sets of MOLS arise from this construction. The projective plane that is associated with the complete set of MOLS obtained from this field construction is a special type, a
2121:= 10 satisfies the conditions, but no projective plane of order 10 exists, as was shown by a very long computer search, which in turn implies that there do not exist nine MOLS of order 10.
383:
A common variant of this problem was to arrange the 16 cards so that, in addition to the row and column constraints, each diagonal contains all four face values and all four suits as well.
1947:. Since the five words cover all 26 letters of the alphabet between them, the table allows for examining each letter of the alphabet in five different typefaces and color combinations.
2307:
46:
if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of
5611:
2471:
4881:
Bose, R. C.; Shrikhande, S. S.; Parker, E. T. (1960), "Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler's conjecture",
1943:
The above table therefore allows for testing five values in each of four different dimensions in only 25 observations instead of 625 (= 5) observations required in a
402:. Each of the 144 solutions has eight reflections and rotations, giving 1152 solutions in total. The 144×8 solutions can be categorized into the following two
7556:
573:
regiments so that they are ranged in a square so that in each line (both horizontal and vertical) there are 6 officers of different ranks and different regiments.
2113:
must be the sum of two (integer) squares. This rules out projective planes of orders 6 and 14 for instance, but does not guarantee the existence of a plane when
8061:
5698:
606:
is odd or a multiple of 4. Observing that no order two square exists and being unable to construct an order six square, he conjectured that none exist for any
207:
692:
In the
November 1959 edition of Scientific American, Martin Gardner published this result. The front cover is the 10 Ă 10 refutation of Euler's conjecture.
8211:
7835:
371:
Although recognized for his original mathematical treatment of the subject, orthogonal Latin squares predate Euler. In the form of an old puzzle involving
2323:
6476:
2157:
6023:
2421:
7609:
8048:
726:
A set of Latin squares of the same order such that every pair of squares are orthogonal (that is, form a Graeco-Latin square) is called a set of
4823:
Bose, R. C.; Shrikhande, S. S. (1959), "On the falsity of Euler's conjecture about the non-existence of two orthogonal Latin squares of order 4
4500:
Mutually orthogonal Latin squares have a great variety of applications. They are used as a starting point for constructions in the statistical
2124:
No other existence results are known. As of 2020, the smallest order for which the existence of a complete set of MOLS is undetermined is 12.
5571:
5526:
5398:
4639:
345:
Thus Graeco-Latin squares exist for all odd orders as there are groups that exist of these orders. Such Graeco-Latin squares are said to be
323:. In an arbitrary Latin square, a selection of positions, one in each row and one in each column whose entries are all distinct is called a
6471:
6171:
5543:
700:
5034:
2091:
7075:
6223:
6047:
552:
Generalisation of the 36 officers puzzle for 1 to 8 ranks (chess pieces) and regiments (colours) – cases 2 and 6 have no solutions
8463:
4150:
For example, using the (5,4)-net of the previous section we can construct a T transversal design. The block associated with the point (
352:
Euler was able to construct Graeco-Latin squares of orders that are multiples of four, and seemed to be aware of the following result.
2540:, and so, has a generator, λ, meaning that all the non-zero elements of the field can be expressed as distinct powers of λ. Name the
7858:
7750:
6098:
5936:
5691:
5553:
5445:
5416:
5260:
4147:
so that two points in the same group are not contained in a block while two points in different groups belong to exactly one block.
2744:
8036:
7910:
1980:) in standard form and examining the entries in the second row and first column of each square, it can be seen that no more than
593:
233:. A Graeco-Latin square can therefore be decomposed into two orthogonal Latin squares. Orthogonality here means that every pair
8094:
7755:
7500:
6871:
6461:
6111:
5819:
5805:
4981:
Goyeneche, Dardo; Raissi, Zahra; Di
Martino, Sara; ƻyczkowski, Karol (2018), "Entanglement and quantum combinatorial designs",
2397:⥠2 (mod 4), that is, there is a single 2 in the prime factorization, the theorem gives a lower bound of 1, which is beaten if
7085:
8145:
7357:
7164:
7053:
7011:
6116:
4509:
4093:
in precisely one variety, and any pair of varieties which belong to different groups occur together in precisely λ blocks in
6250:
1839:
is a representation of the compounded MOLS(5) example above where the four MOLS have the following alphabets, respectively:
600:
Euler was unable to solve the problem, but in this work he demonstrated methods for constructing Graeco-Latin squares where
588:
8388:
7347:
5454:
5183:
4113:
3532:
More general orthogonal arrays represent generalizations of the concept of MOLS, such as mutually orthogonal Latin cubes.
7397:
319:
When a Graeco-Latin square is viewed as a pair of orthogonal Latin squares, each of the Latin squares is said to have an
7939:
7888:
7873:
7863:
7732:
7604:
7571:
7352:
7182:
6017:
5982:
5914:
5770:
5684:
8008:
7309:
3653:
points of the net. Each other column (that is, Latin square) will be used to define the lines in a parallel class. The
3509:
values is filled with the entry in that position in each of the Latin squares. This process is reversible; given an OA(
8283:
8084:
7063:
6732:
6196:
6138:
6087:
5999:
5242:
4467:
3568:
with the property that two distinct lines intersect in at most one point. Moreover, the lines can be partitioned into
1640:
While it is possible to represent MOLS in a "compound" matrix form similar to the Graeco-Latin squares, for instance,
8168:
8135:
4706:
629:. However, Euler's conjecture resisted solution until the late 1950s, but the problem has led to important work in
8140:
7883:
7642:
7548:
7528:
7436:
7147:
6965:
6448:
6320:
5895:
7314:
7080:
6938:
7900:
7668:
7389:
7243:
7172:
7092:
6950:
6931:
6639:
6360:
671:
In April 1959, Parker, Bose, and
Shrikhande presented their paper showing Euler's conjecture to be false for all
391:
8013:
2075:
of the same order, this equivalence can also be expressed in terms of the existence of these projective planes.
8383:
8150:
7698:
7663:
7627:
7412:
6854:
6763:
6722:
6634:
6325:
6164:
6073:
6068:
6033:
5917:
5835:
5790:
5785:
2253:
715:
7420:
7404:
4521:
1736:
for the MOLS(5) example above, it is more typical to compactly represent the MOLS as an orthogonal array (see
718:
code, allowing to encode a 6-level system into a three 6-level system that certifies occurrence of one error.
8292:
7905:
7845:
7782:
7142:
7004:
6994:
6844:
6758:
6041:
2736:). The MOLS(4) and MOLS(5) examples above arose from this construction, although with a change of alphabet.
2680:
2072:
331:
A given Latin square of order n possesses an orthogonal mate if and only if it has n disjoint transversals.
8053:
7990:
6028:
8485:
8330:
8260:
7745:
7632:
6629:
6526:
6433:
6312:
6211:
6004:
5948:
5890:
1748:
Any two of text, foreground color, background color and typeface form a pair of orthogonal Latin squares:
607:
206:
182:
8451:
7329:
355:
No group based Graeco-Latin squares can exist if the order is an odd multiple of two (that is, equal to 4
8355:
8297:
8240:
8066:
7959:
7868:
7594:
7478:
7337:
7219:
7211:
7026:
6922:
6900:
6859:
6824:
6791:
6737:
6712:
6667:
6606:
6566:
6368:
6191:
6133:
5977:
5877:
5851:
5830:
5810:
5747:
5730:
5707:
4544:
4501:
194:
55:
8434:
7324:
6123:
4206:. The points of the design are thus denoted by the integers 1, ..., 20. The blocks of the design are:
564:
asked Euler to solve it, since he was residing at her court at the time. This problem is known as the
8278:
7853:
7802:
7778:
7740:
7658:
7637:
7589:
7468:
7446:
7415:
7201:
7152:
7070:
7043:
6999:
6955:
6717:
6493:
6373:
5993:
5931:
5925:
5000:
4940:
4836:
4549:
1944:
399:
8425:
8350:
8273:
7954:
7718:
7711:
7673:
7581:
7561:
7533:
7266:
7132:
7127:
7117:
7109:
6927:
6888:
6778:
6768:
6677:
6456:
6412:
6330:
6255:
6157:
6093:
6058:
5967:
5618:
Java Tool which assists in constructing Graeco-Latin squares (it does not construct them by itself)
5586:
5535:
5505:
5493:
4116:
2408:
For general composite numbers, the number of MOLS is not known. The first few values starting with
711:
626:
561:
339:
8000:
5617:
4658:
8439:
8250:
8104:
7949:
7825:
7722:
7706:
7683:
7460:
7194:
7177:
7137:
7048:
6943:
6905:
6876:
6836:
6796:
6742:
6659:
6345:
6340:
6128:
5735:
5661:
5481:
5200:
5157:
5016:
4990:
4964:
4930:
2740:
616:
5053:"Centuries-old 'impossible' math problem cracked using the strange physics of Schrödinger's cat"
2447:
17:
8345:
8315:
8307:
8127:
8118:
8043:
7974:
7830:
7815:
7790:
7678:
7619:
7485:
7473:
7099:
7016:
6960:
6883:
6727:
6649:
6428:
6302:
5885:
5872:
5862:
5775:
5752:
5744:
5740:
5715:
5594:
5567:
5549:
5522:
5441:
5412:
5394:
5256:
5174:
4956:
4864:
4666:
4635:
403:
246:
92:
4629:
2686:, the naming convention above can be dropped and the construction rule can be simplified to L
8370:
8325:
8089:
8076:
7969:
7944:
7878:
7810:
7688:
7296:
7189:
7122:
7035:
6982:
6801:
6672:
6466:
6265:
6232:
6063:
5757:
5473:
5248:
5192:
5147:
5008:
4948:
4890:
4854:
4844:
2756:
2042:
665:
641:
637:
5426:
5052:
4904:
3641:). The ordered pairs of entries in each row of the orthogonal array in the columns labeled
8287:
8031:
7893:
7820:
7495:
7369:
7342:
7319:
7288:
6915:
6910:
6864:
6594:
6245:
6079:
6009:
5962:
5422:
4900:
5138:
Bruck, R.H.; Ryser, H.J. (1949), "The nonexistence of certain finite projective planes",
5004:
4944:
4840:
4728:
592:
Redrawing of the
November 1959 Scientific American order-10 Graeco-Latin square –
8236:
8231:
6694:
6624:
6270:
5765:
5539:
5433:
5387:
4505:
4485:
2010:
1860:
661:
557:
387:
376:
308:
291:
262:
5597:
4859:
3501:
denote the row and column of a position in a square and the rest of the row for fixed
2747:
and their corresponding complete sets of MOLS can not be obtained from finite fields.
8479:
8393:
8360:
8223:
8184:
7995:
7964:
7428:
7382:
6987:
6689:
6516:
6280:
6275:
5903:
5845:
5780:
5161:
4968:
4517:
3529:
roles and then fill out the Latin squares with the entries in the remaining columns.
2030:
630:
51:
31:
6546:
5020:
4634:, vol. 4A: Combinatorial Algorithms Part 1, Addison-Wesley, pp. xv+883pp,
2380:{\displaystyle \geq {\underset {i}{\operatorname {min} }}\{p_{i}^{\alpha _{i}}-1\}.}
398:. This mistake persisted for many years until the correct value of 144 was found by
328:
the first square correspond to a transversal in the second square (and vice versa).
223:-coordinates by themselves (which may be thought of as Latin characters) and of the
8335:
8268:
8245:
8160:
7490:
6786:
6684:
6619:
6561:
6483:
6438:
6053:
5621:
4952:
4539:
4513:
2537:
2514:
2058:
2006:
1874:
649:
622:
548:
372:
335:
230:
123:
35:
2239:{\displaystyle n=p_{1}^{\alpha _{1}}p_{2}^{\alpha _{2}}\cdots p_{r}^{\alpha _{r}}}
5485:
3681:
will be those with coordinates corresponding to the rows where the entry in the L
8378:
8340:
8023:
7924:
7786:
7599:
7566:
7058:
6975:
6970:
6614:
6571:
6551:
6531:
6521:
6290:
5909:
5840:
5825:
5795:
5657:
5626:
5458:
4738:
2090:
The only general result on the non-existence of finite projective planes is the
5012:
2513:
is a prime or prime power. This follows from a construction that is based on a
7224:
6704:
6404:
6335:
6285:
6260:
6180:
5725:
5646:
5178:
4734:
4512:. Euler's interest in Graeco-Latin squares arose from his desire to construct
1936:
1928:
1924:
710:
physicists (Rather, Burchardt, Bruzda, Rajchel-MieldzioÄ, Lakshminarayan, and
395:
5634:
5252:
4646:
7377:
7229:
6849:
6644:
6556:
6541:
6536:
6501:
5857:
5602:
2679:
a prime), where the field elements are represented in the usual way, as the
1856:
653:
5635:
Javascript
Application to solve Graeco-Latin Squares from size 1x1 to 10x10
5152:
4960:
4895:
4868:
4849:
2393:
MacNeish's theorem does not give a very good lower bound, for instance if
6893:
6511:
6388:
6383:
6378:
6350:
5638:
5489:|doi-broken-date=2020-10-03| zbl=1112.05018 | citeseerx=10.1.1.151.3043}}
652:
found a counterexample of order 10 using a one-hour computer search on a
5676:
8398:
8099:
5204:
4534:
4163:. The points of the design will be obtained from the following scheme:
1932:
5477:
4794:
Compte Rendu de l'Association Française pour l'Avancement des
Sciences
4775:
Compte Rendu de l'Association Française pour l'Avancement des
Sciences
394:, the number of distinct solutions was incorrectly stated to be 72 by
342:
of odd order forms a Latin square which possesses an orthogonal mate.
8320:
7301:
7275:
7255:
6506:
6297:
5589:
AMS featured column archive (Latin
Squares in Practice and Theory II)
5438:
Martin
Gardner's New Mathematical Diversions from Scientific American
1955:
The mutual orthogonality property of a set of MOLS is unaffected by
1907:
1901:
1895:
1882:
1848:
657:
5196:
4995:
4935:
2830:). For example, the MOLS(4) example given above and repeated here,
173:
exactly once, and that no two cells contain the same ordered pair.
5035:"Euler's 243-Year-Old 'Impossible' Puzzle Gets a Quantum Solution"
3691:. There are two additional parallel classes, corresponding to the
1920:
1889:
1866:
1844:
587:
547:
5498:
Constructions and
Combinatorial Problems in Design of Experiments
2071:
below). As every finite affine plane is uniquely extendable to a
664:(this was one of the earliest combinatorics problems solved on a
6240:
2017:). However, the number of MOLS that may exist for a given order
1913:
1878:
1852:
621:
The non-existence of order six squares was confirmed in 1901 by
390:, who featured this variant of the problem in his November 1959
161:, such that every row and every column contains each element of
8209:
7776:
7523:
6822:
6592:
6209:
6153:
5680:
5500:(corrected reprint of the 1971 Wiley ed.), New York: Dover
2803:), every ordered pair of symbols appears in exactly one row of
2401:> 6. On the other hand, it does give the correct value when
556:
A problem similar to the card problem above was circulating in
4101:
The existence of a T design is equivalent to the existence of
1870:
6149:
4060:, but not in the algebraic sense) which form a partition of
3572:
parallel classes (no two of its lines meet) each containing
2148:= 2 or 6, where it is 1. However, more can be said, namely,
1962:
Permuting the columns of all the squares simultaneously, and
596:
hover over the letters to hide the background and vice versa
2416:
61:
An outdated term for pair of orthogonal Latin squares is
5641:(Javascript in Firefox browser and HTML5 mobile devices)
5241:
Lenz, H.; Jungnickel, D.; Beth, Thomas (November 1999).
4915:
4913:
2621:-1). The Latin squares are constructed as follows, the (
2587:
Now, λ = 1 and the product rule in terms of the α's is α
1969:
Using these operations, any set of MOLS can be put into
177:
Graeco-Latin squares (pairs of orthogonal Latin squares)
5510:
Block Designs: Analysis, Combinatorics and Applications
2528:
is a prime or prime power. The multiplicative group of
2414:= 2, 3, 4... are 1, 2, 3, 4, 1, 6, 7, 8, ... (sequence
408:
5179:"The Search for a Finite Projective Plane of Order 10"
4730:
Recherches sur une nouvelle espece de quarres magiques
3063:
2952:
2841:
1486:
1346:
1206:
1066:
948:
854:
760:
5633:
Historical facts and correlation with Magic Squares,
5393:(2nd ed.), Boca Raton: Chapman & Hall/ CRC,
4792:
Tarry, Gaston (1901). "Le Probléme de 36 Officiers".
4773:
Tarry, Gaston (1900). "Le Probléme de 36 Officiers".
4711:
Proceedings of the Royal Institution of Great Britain
4569:
This has gone under several names in the literature,
2839:
2450:
2427:
The smallest case for which the exact number of MOLS(
2326:
2256:
2160:
1959:
Permuting the rows of all the squares simultaneously,
1064:
758:
8062:
Autoregressive conditional heteroskedasticity (ARCH)
722:
Examples of mutually orthogonal Latin squares (MOLS)
8369:
8306:
8259:
8222:
8177:
8159:
8126:
8117:
8075:
8022:
7983:
7932:
7923:
7844:
7801:
7731:
7697:
7651:
7618:
7580:
7547:
7459:
7368:
7287:
7242:
7210:
7163:
7108:
7034:
7025:
6835:
6777:
6751:
6703:
6658:
6605:
6492:
6447:
6421:
6403:
6359:
6311:
6231:
6222:
5976:
5871:
5804:
5714:
5228:
5092:
4829:
Proceedings of the National Academy of Sciences USA
4707:"Magic Squares and Other Problems on a Chess Board"
1965:
Permuting the entries in any square, independently.
375:, the construction of a 4 x 4 set was published by
261:Orthogonal Latin squares were studied in detail by
5519:Combinatorial Designs / Constructions and Analysis
5386:
3717:consist of the points whose first coordinates are
3649:, will be considered to be the coordinates of the
3173:
2465:
2379:
2301:
2238:
1629:
1044:
5628:Anything but square: from magic squares to Sudoku
5385:Colbourn, Charles J.; Dinitz, Jeffrey H. (2007),
3629:), represent the MOLS as an orthogonal array, OA(
2094:, which says that if a projective plane of order
648:) of order 22 using mathematical insights. Then
229:-coordinates (the Greek characters) each forms a
5411:, New York-London: Academic Press, p. 547,
2671:). In the case that the field is a prime field (
2043:Projective plane § Finite projective planes
678:Thus, Graeco-Latin squares exist for all orders
7610:Multivariate adaptive regression splines (MARS)
5612:Euler's work on Latin Squares and Euler Squares
3725:respectively. This construction is reversible.
2791:â„ 1, integers) with entries from a set of size
1951:The number of mutually orthogonal Latin squares
570:
299: = {α , ÎČ, Îł, ...
5368:
5320:
5080:
5068:
4810:
4760:
4692:
2014:
560:in the late 1700s and, according to folklore,
122:arrangement of cells, each cell containing an
6165:
5692:
5332:
5293:
5281:
5216:
5116:
5104:
4615:
4603:
4586:
644:constructed some counterexamples (dubbed the
8:
5459:"Small Latin Squares, Quasigroups and Loops"
5356:
5344:
4466:) is equivalent to an edge-partition of the
2371:
2340:
106:(which may be the same), each consisting of
5587:Leonhard Euler's Puzzle of the 36 Officiers
749:For example, a set of MOLS(4) is given by:
311:—hence the name Graeco-Latin square.
8219:
8206:
8123:
7929:
7798:
7773:
7544:
7520:
7248:
7031:
6832:
6819:
6602:
6589:
6228:
6219:
6206:
6172:
6158:
6150:
5699:
5685:
5677:
5457:; Meynert, Alison; Myrvold, Wendy (2007),
5304:
5302:
2078:As mentioned above, complete sets of MOLS(
5151:
4994:
4934:
4894:
4858:
4848:
4676:
4674:
4524:around a 10×10 Graeco-Latin square.
3493:where the entries in the columns labeled
3159:
3062:
3048:
2951:
2937:
2840:
2838:
2456:
2451:
2449:
2357:
2352:
2347:
2330:
2325:
2302:{\displaystyle p_{1},p_{2},\cdots ,p_{r}}
2293:
2274:
2261:
2255:
2228:
2223:
2218:
2203:
2198:
2193:
2181:
2176:
2171:
2159:
1485:
1345:
1205:
1065:
1063:
947:
853:
759:
757:
4800:. SecrĂ©tariat de l'Association: 170â203.
4781:. SecrĂ©tariat de l'Association: 122â123.
4756:
4754:
4752:
4750:
4748:
4746:
4421:
4210:
3732:
3657:lines determined by the column labeled L
3521:â„ 3, choose any two columns to play the
3188:
2117:satisfies the condition. In particular,
1999:. Complete sets are known to exist when
1644:
699:
5308:
4680:
4599:
4597:
4595:
4562:
2769:), of strength two and index one is an
656:Military Computer while working at the
583:
175:
8136:KaplanâMeier estimator (product limit)
568:, and Euler introduced it as follows:
54:is strongly related to the concept of
5562:van Lint, J.H.; Wilson, R.M. (1993),
4660:Recreation mathematiques et physiques
4143:equivalence classes (groups) of size
4006:and index λ, denoted T, is a triple (
3638:
2491:. Moreover, the minimum is 6 for all
2444:, the number of MOLS is greater than
1737:
696:Thirty-six entangled officers problem
7:
8446:
8146:Accelerated failure time (AFT) model
5545:Combinatorics of Experimental Design
5409:Latin squares and their applications
4510:error correcting and detecting codes
2795:such that within any two columns of
2663:, where all the operations occur in
2479:, there are only a finite number of
2246:is the factorization of the integer
8458:
7741:Analysis of variance (ANOVA, anova)
6048:Generalized randomized block design
5407:DĂ©nes, J.; Keedwell, A. D. (1974),
7836:CochranâMantelâHaenszel statistics
6462:Pearson product-moment correlation
3587:)-net is an affine plane of order
2745:non-Desarguesian projective planes
25:
6099:Sequential probability ratio test
5389:Handbook of Combinatorial Designs
5229:McKay, Meynert & Myrvold 2007
5093:McKay, Meynert & Myrvold 2007
746:when the order is made explicit.
732:pairwise orthogonal Latin squares
728:mutually orthogonal Latin squares
48:mutually orthogonal Latin squares
8457:
8445:
8433:
8420:
8419:
6122:
6024:Polynomial and rational modeling
5466:Journal of Combinatorial Designs
3184:can be used to form an OA(5,4):
2485:such that the number of MOLS is
2029:, and is an area of research in
530:
511:
495:
488:
462:
458:
439:
429:
205:
193:
181:
18:Mutually orthogonal latin square
8095:Least-squares spectral analysis
5664:from the original on 2021-12-12
5140:Canadian Journal of Mathematics
4883:Canadian Journal of Mathematics
4631:The Art of Computer Programming
3061:
3060:
2950:
2949:
2250:into powers of distinct primes
2015:Finite field construction below
1484:
1344:
1204:
946:
945:
852:
851:
584:Euler's conjecture and disproof
7076:Mean-unbiased minimum-variance
5791:Replication versus subsampling
5566:, Cambridge University Press,
4953:10.1103/PhysRevLett.128.080507
4112:A transversal design T is the
4078:) of varieties such that each
524:
521:
517:
514:
504:
501:
485:
482:
471:
468:
452:
449:
445:
442:
426:
423:
359:+ 2 for some positive integer
265:, who took the two sets to be
52:orthogonality in combinatorics
1:
8389:Geographic information system
7605:Simultaneous equations models
5184:American Mathematical Monthly
4154:) of the net will be denoted
4139:points. The points fall into
2741:Desarguesian projective plane
734:) and usually abbreviated as
527:
508:
498:
491:
465:
455:
436:
432:
65:, found in older literature.
7572:Coefficient of determination
7183:Uniformly most powerful test
6018:Response surface methodology
5926:Analysis of variance (Anova)
5517:Stinson, Douglas R. (2004),
5508:& Padgett, L.V. (2005).
5244:Design Theory by Thomas Beth
4135:blocks; each block contains
3721:, or second coordinates are
2728:) and all operations are in
2057:) is equivalent to a finite
1987:squares can exist. A set of
1832:
1829:
1826:
1823:
1820:
1815:
1812:
1809:
1806:
1803:
1798:
1795:
1792:
1789:
1786:
1781:
1778:
1775:
1772:
1769:
1764:
1761:
1758:
1755:
1752:
481:
422:
307:lower-case letters from the
290:upper-case letters from the
8141:Proportional hazards models
8085:Spectral density estimation
8067:Vector autoregression (VAR)
7501:Maximum posterior estimator
6733:Randomized controlled trial
6088:Randomized controlled trial
4663:, vol. IV, p. 434
2625:)th entry in Latin square L
2316:the minimum number of MOLS(
2136:) is known to be 2 for all
2132:The minimum number of MOLS(
566:thirty-six officers problem
544:Thirty-six officers problem
8502:
7901:Multivariate distributions
6321:Average absolute deviation
5369:van Lint & Wilson 1993
5321:Colbourn & Dinitz 2007
5081:Colbourn & Dinitz 2007
5069:Colbourn & Dinitz 2007
5051:Pappas, Stephanie (2022),
5013:10.1103/PhysRevA.97.062326
4811:van Lint & Wilson 1993
4761:Colbourn & Dinitz 2007
4693:van Lint & Wilson 1993
4520:structured his 1978 novel
2754:
2466:{\displaystyle {\sqrt{n}}}
2040:
8415:
8218:
8205:
7889:Structural equation model
7797:
7772:
7543:
7519:
7251:
7225:Score/Lagrange multiplier
6831:
6818:
6640:Sample size determination
6601:
6588:
6218:
6205:
6187:
6107:
5564:A Course in Combinatorics
5333:DĂ©nes & Keedwell 1974
5294:DĂ©nes & Keedwell 1974
5282:DĂ©nes & Keedwell 1974
5217:DĂ©nes & Keedwell 1974
5117:DĂ©nes & Keedwell 1974
5105:DĂ©nes & Keedwell 1974
4616:DĂ©nes & Keedwell 1974
4604:DĂ©nes & Keedwell 1974
4587:DĂ©nes & Keedwell 1974
4131:blocks. Each point is in
2501:Finite field construction
2092:Bruck–Ryser theorem
2068:
2023:is not known for general
1976:By putting a set of MOLS(
414:
411:
392:Mathematical Games column
338:(without borders) of any
32:combinatorial mathematics
8384:Environmental statistics
7906:Elliptical distributions
7699:Generalized linear model
7628:Simple linear regression
7398:HodgesâLehmann estimator
6855:Probability distribution
6764:Stochastic approximation
6326:Coefficient of variation
6074:Repeated measures design
5786:Restricted randomization
5357:Street & Street 1987
5345:Street & Street 1987
5253:10.1017/cbo9781139507660
4657:Ozanam, Jacques (1725),
3981:(1,4) (2,4) (3,4) (4,4)
3969:(1,3) (2,3) (3,3) (4,3)
3957:(1,2) (2,2) (3,2) (4,2)
3945:(1,1) (2,1) (3,1) (4,1)
3931:(4,1) (4,2) (4,3) (4,4)
3919:(3,1) (3,2) (3,3) (3,4)
3907:(2,1) (2,2) (2,3) (2,4)
3895:(1,1) (1,2) (1,3) (1,4)
3881:(1,4) (2,2) (3,1) (4,3)
3869:(1,3) (2,1) (3,2) (4,4)
3857:(1,2) (2,4) (3,3) (4,1)
3845:(1,1) (2,3) (3,4) (4,2)
3831:(1,4) (2,1) (3,3) (4,2)
3819:(1,3) (2,2) (3,4) (4,1)
3807:(1,2) (2,3) (3,1) (4,4)
3795:(1,1) (2,4) (3,2) (4,3)
3781:(1,4) (2,3) (3,2) (4,1)
3769:(1,3) (2,4) (3,1) (4,2)
3757:(1,2) (2,1) (3,4) (4,3)
3745:(1,1) (2,2) (3,3) (4,4)
83:orthogonal Latin squares
8044:Cross-correlation (XCF)
7652:Non-standard predictors
7086:LehmannâScheffĂ© theorem
6759:Adaptive clinical trial
4923:Physical Review Letters
4705:P. A. MacMahon (1902).
4417:The five "groups" are:
4123:)-net. That is, it has
2524:), which only exist if
2505:A complete set of MOLS(
2405:is a power of a prime.
2127:
2073:finite projective plane
716:quantum error detection
217:The arrangement of the
8440:Mathematics portal
8261:Engineering statistics
8169:NelsonâAalen estimator
7746:Analysis of covariance
7633:Ordinary least squares
7557:Pearson product-moment
6961:Statistical functional
6872:Empirical distribution
6705:Controlled experiments
6434:Frequency distribution
6212:Descriptive statistics
6129:Mathematics portal
5891:Ordinary least squares
5153:10.4153/cjm-1949-009-2
4896:10.4153/CJM-1960-016-5
4628:Knuth, Donald (2011),
4086:intersects each group
3602:) is equivalent to a (
3175:
2467:
2381:
2303:
2240:
1865:the foreground color:
1843:the background color:
1631:
1055:And a set of MOLS(5):
1046:
706:
597:
581:
553:
56:blocking in statistics
8356:Population statistics
8298:System identification
8032:Autocorrelation (ACF)
7960:Exponential smoothing
7874:Discriminant analysis
7869:Canonical correlation
7733:Partition of variance
7595:Regression validation
7439:(JonckheereâTerpstra)
7338:Likelihood-ratio test
7027:Frequentist inference
6939:Locationâscale family
6860:Sampling distribution
6825:Statistical inference
6792:Cross-sectional study
6779:Observational studies
6738:Randomized experiment
6567:Stem-and-leaf display
6369:Central limit theorem
5726:Scientific experiment
5708:Design of experiments
5033:Garisto, Dan (2022),
4850:10.1073/pnas.45.5.734
4665:, the solution is in
4545:Blocking (statistics)
4522:Life: A User's Manual
4506:tournament scheduling
4502:design of experiments
3176:
2468:
2382:
2304:
2241:
1945:full factorial design
1919:the typeface family:
1632:
1047:
703:
591:
551:
258:occurs exactly once.
8279:Probabilistic design
7864:Principal components
7707:Exponential families
7659:Nonlinear regression
7638:General linear model
7600:Mixed effects models
7590:Errors and residuals
7567:Confounding variable
7469:Bayesian probability
7447:Van der Waerden test
7437:Ordered alternative
7202:Multiple comparisons
7081:RaoâBlackwellization
7044:Estimating equations
7000:Statistical distance
6718:Factorial experiment
6251:Arithmetic-Geometric
6000:Fractional factorial
5598:"36 Officer Problem"
5536:Street, Anne Penfold
5506:Raghavarao, Damaraju
5494:Raghavarao, Damaraju
4550:Combinatorial design
4516:. The French writer
2837:
2448:
2324:
2254:
2158:
1997:complete set of MOLS
1062:
756:
400:Kathleen Ollerenshaw
167:and each element of
69:Graeco-Latin squares
27:Mathematical problem
8351:Official statistics
8274:Methods engineering
7955:Seasonal adjustment
7723:Poisson regressions
7643:Bayesian regression
7582:Regression analysis
7562:Partial correlation
7534:Regression analysis
7133:Prediction interval
7128:Likelihood interval
7118:Confidence interval
7110:Interval estimation
7071:Unbiased estimators
6889:Model specification
6769:Up-and-down designs
6457:Partial correlation
6413:Index of dispersion
6331:Interquartile range
6134:Statistical outline
6094:Sequential analysis
6059:Graeco-Latin square
5968:Multiple comparison
5915:Hierarchical model:
5512:. World Scientific.
5005:2018PhRvA..97f2326G
4945:2022PhRvL.128h0507R
4841:1959PNAS...45..734B
4117:incidence structure
3990:Transversal designs
3699:columns. The lines
3663:will be denoted by
2822:) is equivalent to
2364:
2235:
2210:
2188:
1749:
627:proof by exhaustion
562:Catherine the Great
404:equivalence classes
75:Graeco-Latin square
63:Graeco-Latin square
8371:Spatial statistics
8251:Medical statistics
8151:First hitting time
8105:Whittle likelihood
7756:Degrees of freedom
7751:Multivariate ANOVA
7684:Heteroscedasticity
7496:Bayesian estimator
7461:Bayesian inference
7310:KolmogorovâSmirnov
7195:Randomization test
7165:Testing hypotheses
7138:Tolerance interval
7049:Maximum likelihood
6944:Exponential family
6877:Density estimation
6837:Statistical theory
6797:Natural experiment
6743:Scientific control
6660:Survey methodology
6346:Standard deviation
6139:Statistical topics
5731:Statistical design
5595:Weisstein, Eric W.
5540:Street, Deborah J.
5247:. Cambridge Core.
4486:complete subgraphs
4472:+ 2)-partite graph
3996:transversal design
3544:)-net is a set of
3171:
3169:
3058:
2947:
2509:) exists whenever
2463:
2431:) is not known is
2377:
2343:
2338:
2299:
2236:
2214:
2189:
2167:
2152:MacNeish's Theorem
2109:⥠2 (mod 4), then
1747:
1627:
1622:
1482:
1342:
1202:
1042:
1037:
943:
849:
707:
598:
554:
50:. This concept of
38:of the same size (
8473:
8472:
8411:
8410:
8407:
8406:
8346:National accounts
8316:Actuarial science
8308:Social statistics
8201:
8200:
8197:
8196:
8193:
8192:
8128:Survival function
8113:
8112:
7975:Granger causality
7816:Contingency table
7791:Survival analysis
7768:
7767:
7764:
7763:
7620:Linear regression
7515:
7514:
7511:
7510:
7486:Credible interval
7455:
7454:
7238:
7237:
7054:Method of moments
6923:Parametric family
6884:Statistical model
6814:
6813:
6810:
6809:
6728:Random assignment
6650:Statistical power
6584:
6583:
6580:
6579:
6429:Contingency table
6399:
6398:
6266:Generalized/power
6147:
6146:
6034:Central composite
5932:Cochran's theorem
5886:Linear regression
5863:Nuisance variable
5776:Random assignment
5753:Experimental unit
5573:978-0-521-42260-4
5548:, Oxford U. P. ,
5528:978-0-387-95487-5
5478:10.1002/jcd.20105
5455:McKay, Brendan D.
5400:978-1-58488-506-1
4983:Physical Review A
4827: + 2",
4739:published in 1782
4641:978-0-201-03804-0
4585:amongst others. (
4571:formule directrix
4449:
4448:
4413:
4412:
4052:} is a family of
3985:
3984:
3489:
3488:
2473:, thus for every
2461:
2438:For large enough
2331:
2128:McNeish's theorem
2037:Projective planes
1837:
1836:
1732:
1731:
683: > 1
537:
536:
247:Cartesian product
42:) are said to be
16:(Redirected from
8493:
8461:
8460:
8449:
8448:
8438:
8437:
8423:
8422:
8326:Crime statistics
8220:
8207:
8124:
8090:Fourier analysis
8077:Frequency domain
8057:
8004:
7970:Structural break
7930:
7879:Cluster analysis
7826:Log-linear model
7799:
7774:
7715:
7689:Homoscedasticity
7545:
7521:
7440:
7432:
7424:
7423:(KruskalâWallis)
7408:
7393:
7348:Cross validation
7333:
7315:AndersonâDarling
7262:
7249:
7220:Likelihood-ratio
7212:Parametric tests
7190:Permutation test
7173:1- & 2-tails
7064:Minimum distance
7036:Point estimation
7032:
6983:Optimal decision
6934:
6833:
6820:
6802:Quasi-experiment
6752:Adaptive designs
6603:
6590:
6467:Rank correlation
6229:
6220:
6207:
6174:
6167:
6160:
6151:
6127:
6126:
6064:Orthogonal array
5701:
5694:
5687:
5678:
5673:
5671:
5669:
5651:
5608:
5607:
5576:
5558:
5531:
5513:
5501:
5488:
5463:
5450:
5429:
5403:
5392:
5372:
5366:
5360:
5354:
5348:
5342:
5336:
5330:
5324:
5318:
5312:
5306:
5297:
5291:
5285:
5279:
5273:
5272:
5270:
5269:
5238:
5232:
5226:
5220:
5214:
5208:
5207:
5171:
5165:
5164:
5155:
5135:
5129:
5126:
5120:
5114:
5108:
5102:
5096:
5090:
5084:
5078:
5072:
5066:
5060:
5059:
5048:
5042:
5041:
5030:
5024:
5023:
4998:
4978:
4972:
4971:
4938:
4917:
4908:
4907:
4898:
4878:
4872:
4871:
4862:
4852:
4820:
4814:
4808:
4802:
4801:
4789:
4783:
4782:
4770:
4764:
4758:
4741:
4725:
4719:
4718:
4702:
4696:
4690:
4684:
4678:
4669:
4664:
4654:
4648:
4644:
4625:
4619:
4613:
4607:
4601:
4590:
4567:
4491:
4471:
4465:
4461:
4422:
4402:
4390:
4378:
4366:
4352:
4340:
4328:
4316:
4302:
4290:
4278:
4266:
4252:
4240:
4228:
4216:
4211:
4205:
4201:
4192:
4188:
4179:
4175:
4166:
4157:
4153:
4146:
4142:
4138:
4134:
4130:
4126:
4122:
4108:
4104:
4096:
4092:
4085:
4081:
4073:
4069:
4063:
4055:
4051:
4020:
4016:
4009:
4005:
4001:
3974:
3962:
3950:
3938:
3924:
3912:
3900:
3888:
3874:
3862:
3850:
3838:
3824:
3812:
3800:
3788:
3774:
3762:
3750:
3738:
3733:
3724:
3720:
3711:
3702:
3698:
3694:
3690:
3672:. The points on
3656:
3652:
3648:
3644:
3636:
3632:
3628:
3624:
3620:
3616:
3613:To construct a (
3609:
3605:
3601:
3597:
3590:
3586:
3582:
3575:
3571:
3567:
3555:
3548:elements called
3547:
3543:
3520:
3516:
3512:
3189:
3180:
3178:
3177:
3172:
3170:
3167:
3166:
3164:
3163:
3153:
3059:
3056:
3055:
3053:
3052:
3042:
2948:
2945:
2944:
2942:
2941:
2931:
2829:
2825:
2821:
2817:
2806:
2798:
2794:
2790:
2786:
2782:
2778:
2768:
2763:orthogonal array
2757:Orthogonal array
2751:Orthogonal array
2735:
2727:
2720:are elements of
2719:
2715:
2711:
2707:
2703:
2699:
2695:
2690:
2684:
2681:integers modulo
2678:
2674:
2670:
2661:
2655:
2649:
2644:
2639:
2634:
2629:
2624:
2620:
2616:
2612:
2608:
2603:
2597:
2591:
2578:
2551:
2543:
2535:
2527:
2523:
2512:
2508:
2496:
2490:
2484:
2478:
2472:
2470:
2469:
2464:
2462:
2460:
2452:
2443:
2434:
2430:
2419:
2413:
2404:
2400:
2396:
2387:
2386:
2384:
2383:
2378:
2363:
2362:
2361:
2351:
2339:
2319:
2308:
2306:
2305:
2300:
2298:
2297:
2279:
2278:
2266:
2265:
2249:
2245:
2243:
2242:
2237:
2234:
2233:
2232:
2222:
2209:
2208:
2207:
2197:
2187:
2186:
2185:
2175:
2147:
2141:
2135:
2120:
2116:
2112:
2108:
2104:
2102:
2097:
2085:
2081:
2066:
2056:
2052:
2028:
2022:
2013:of a prime (see
2004:
1994:
1990:
1986:
1984:
1979:
1750:
1746:
1645:
1636:
1634:
1633:
1628:
1623:
1483:
1343:
1203:
1051:
1049:
1048:
1043:
1038:
944:
850:
691:
684:
677:
666:digital computer
642:S. S. Shrikhande
620:
605:
594:in the SVG file,
579:
532:
529:
526:
523:
519:
516:
513:
510:
506:
503:
500:
497:
493:
490:
487:
484:
473:
470:
467:
464:
460:
457:
454:
451:
447:
444:
441:
438:
434:
431:
428:
425:
409:
362:
358:
306:
300:
289:
283:
257:
244:
228:
222:
209:
197:
185:
172:
166:
160:
154:
148:
142:
136:
121:
111:
105:
99:
90:
21:
8501:
8500:
8496:
8495:
8494:
8492:
8491:
8490:
8476:
8475:
8474:
8469:
8432:
8403:
8365:
8302:
8288:quality control
8255:
8237:Clinical trials
8214:
8189:
8173:
8161:Hazard function
8155:
8109:
8071:
8055:
8018:
8014:BreuschâGodfrey
8002:
7979:
7919:
7894:Factor analysis
7840:
7821:Graphical model
7793:
7760:
7727:
7713:
7693:
7647:
7614:
7576:
7539:
7538:
7507:
7451:
7438:
7430:
7422:
7406:
7391:
7370:Rank statistics
7364:
7343:Model selection
7331:
7289:Goodness of fit
7283:
7260:
7234:
7206:
7159:
7104:
7093:Median unbiased
7021:
6932:
6865:Order statistic
6827:
6806:
6773:
6747:
6699:
6654:
6597:
6595:Data collection
6576:
6488:
6443:
6417:
6395:
6355:
6307:
6224:Continuous data
6214:
6201:
6183:
6178:
6148:
6143:
6121:
6103:
6080:Crossover study
6071:
6069:Latin hypercube
6005:PlackettâBurman
5984:
5981:
5980:
5972:
5875:
5867:
5808:
5800:
5717:
5710:
5705:
5667:
5665:
5649:
5647:"Euler Squares"
5644:
5593:
5592:
5583:
5574:
5561:
5556:
5534:
5529:
5516:
5504:
5492:
5461:
5453:
5448:
5434:Gardner, Martin
5432:
5419:
5406:
5401:
5384:
5381:
5376:
5375:
5367:
5363:
5355:
5351:
5343:
5339:
5331:
5327:
5319:
5315:
5307:
5300:
5292:
5288:
5280:
5276:
5267:
5265:
5263:
5240:
5239:
5235:
5227:
5223:
5215:
5211:
5197:10.2307/2323798
5173:
5172:
5168:
5137:
5136:
5132:
5127:
5123:
5115:
5111:
5103:
5099:
5091:
5087:
5079:
5075:
5067:
5063:
5050:
5049:
5045:
5039:Quanta Magazine
5032:
5031:
5027:
4980:
4979:
4975:
4919:
4918:
4911:
4880:
4879:
4875:
4822:
4821:
4817:
4809:
4805:
4791:
4790:
4786:
4772:
4771:
4767:
4759:
4744:
4735:written in 1779
4726:
4722:
4704:
4703:
4699:
4691:
4687:
4679:
4672:
4656:
4655:
4651:
4642:
4627:
4626:
4622:
4614:
4610:
4602:
4593:
4568:
4564:
4559:
4554:
4530:
4498:
4489:
4483:
4469:
4463:
4459:
4456:
4405:
4400:
4393:
4388:
4381:
4376:
4369:
4364:
4355:
4350:
4343:
4338:
4331:
4326:
4319:
4314:
4305:
4300:
4293:
4288:
4281:
4276:
4269:
4264:
4255:
4250:
4243:
4238:
4231:
4226:
4219:
4214:
4203:
4199:
4197:
4190:
4186:
4184:
4177:
4173:
4171:
4164:
4162:
4155:
4151:
4144:
4140:
4136:
4132:
4128:
4124:
4120:
4106:
4102:
4094:
4091:
4087:
4083:
4079:
4071:
4070:is a family of
4067:
4061:
4053:
4050:
4041:
4034:
4024:
4018:
4014:
4007:
4003:
4002:groups of size
3999:
3992:
3977:
3972:
3965:
3960:
3953:
3948:
3941:
3936:
3927:
3922:
3915:
3910:
3903:
3898:
3891:
3886:
3877:
3872:
3865:
3860:
3853:
3848:
3841:
3836:
3827:
3822:
3815:
3810:
3803:
3798:
3791:
3786:
3777:
3772:
3765:
3760:
3753:
3748:
3741:
3736:
3722:
3718:
3716:
3709:
3707:
3700:
3696:
3692:
3688:
3686:
3680:
3671:
3662:
3654:
3650:
3646:
3642:
3634:
3630:
3626:
3622:
3618:
3614:
3607:
3603:
3599:
3595:
3588:
3584:
3580:
3573:
3569:
3565:
3556:subsets called
3553:
3545:
3541:
3540:A (geometric) (
3538:
3518:
3514:
3510:
3213:
3207:
3201:
3168:
3165:
3155:
3151:
3150:
3145:
3140:
3135:
3129:
3128:
3123:
3118:
3113:
3107:
3106:
3101:
3096:
3091:
3085:
3084:
3079:
3074:
3069:
3057:
3054:
3044:
3040:
3039:
3034:
3029:
3024:
3018:
3017:
3012:
3007:
3002:
2996:
2995:
2990:
2985:
2980:
2974:
2973:
2968:
2963:
2958:
2946:
2943:
2933:
2929:
2928:
2923:
2918:
2913:
2907:
2906:
2901:
2896:
2891:
2885:
2884:
2879:
2874:
2869:
2863:
2862:
2857:
2852:
2847:
2835:
2834:
2827:
2823:
2819:
2815:
2804:
2796:
2792:
2788:
2784:
2780:
2770:
2766:
2759:
2753:
2733:
2725:
2717:
2713:
2709:
2705:
2701:
2697:
2693:
2691:
2688:
2682:
2676:
2672:
2668:
2662:
2659:
2656:
2653:
2650:
2647:
2642:
2640:
2637:
2632:
2630:
2627:
2622:
2618:
2614:
2610:
2606:
2604:
2601:
2598:
2595:
2592:
2589:
2580:
2576:
2573:
2569:
2565:
2561:
2552:) as follows:
2549:
2541:
2533:
2525:
2521:
2510:
2506:
2503:
2492:
2486:
2480:
2474:
2446:
2445:
2439:
2432:
2428:
2415:
2409:
2402:
2398:
2394:
2353:
2322:
2321:
2317:
2315:
2289:
2270:
2257:
2252:
2251:
2247:
2224:
2199:
2177:
2156:
2155:
2143:
2137:
2133:
2130:
2118:
2114:
2110:
2106:
2100:
2099:
2095:
2083:
2079:
2062:
2054:
2048:
2045:
2039:
2024:
2018:
2000:
1992:
1991:− 1 MOLS(
1988:
1982:
1981:
1977:
1953:
1621:
1620:
1615:
1610:
1605:
1600:
1594:
1593:
1588:
1583:
1578:
1573:
1567:
1566:
1561:
1556:
1551:
1546:
1540:
1539:
1534:
1529:
1524:
1519:
1513:
1512:
1507:
1502:
1497:
1492:
1481:
1480:
1475:
1470:
1465:
1460:
1454:
1453:
1448:
1443:
1438:
1433:
1427:
1426:
1421:
1416:
1411:
1406:
1400:
1399:
1394:
1389:
1384:
1379:
1373:
1372:
1367:
1362:
1357:
1352:
1341:
1340:
1335:
1330:
1325:
1320:
1314:
1313:
1308:
1303:
1298:
1293:
1287:
1286:
1281:
1276:
1271:
1266:
1260:
1259:
1254:
1249:
1244:
1239:
1233:
1232:
1227:
1222:
1217:
1212:
1201:
1200:
1195:
1190:
1185:
1180:
1174:
1173:
1168:
1163:
1158:
1153:
1147:
1146:
1141:
1136:
1131:
1126:
1120:
1119:
1114:
1109:
1104:
1099:
1093:
1092:
1087:
1082:
1077:
1072:
1060:
1059:
1036:
1035:
1030:
1025:
1020:
1014:
1013:
1008:
1003:
998:
992:
991:
986:
981:
976:
970:
969:
964:
959:
954:
942:
941:
936:
931:
926:
920:
919:
914:
909:
904:
898:
897:
892:
887:
882:
876:
875:
870:
865:
860:
848:
847:
842:
837:
832:
826:
825:
820:
815:
810:
804:
803:
798:
793:
788:
782:
781:
776:
771:
766:
754:
753:
724:
698:
686:
679:
672:
611:
601:
586:
580:
577:
546:
533:
520:
507:
494:
474:
461:
448:
435:
369:
360:
356:
321:orthogonal mate
317:
302:
295:
285:
266:
249:
234:
224:
218:
213:
210:
201:
198:
189:
186:
168:
162:
156:
150:
144:
138:
126:
113:
112:symbols, is an
107:
101:
95:
86:
71:
28:
23:
22:
15:
12:
11:
5:
8499:
8497:
8489:
8488:
8478:
8477:
8471:
8470:
8468:
8467:
8455:
8443:
8429:
8416:
8413:
8412:
8409:
8408:
8405:
8404:
8402:
8401:
8396:
8391:
8386:
8381:
8375:
8373:
8367:
8366:
8364:
8363:
8358:
8353:
8348:
8343:
8338:
8333:
8328:
8323:
8318:
8312:
8310:
8304:
8303:
8301:
8300:
8295:
8290:
8281:
8276:
8271:
8265:
8263:
8257:
8256:
8254:
8253:
8248:
8243:
8234:
8232:Bioinformatics
8228:
8226:
8216:
8215:
8210:
8203:
8202:
8199:
8198:
8195:
8194:
8191:
8190:
8188:
8187:
8181:
8179:
8175:
8174:
8172:
8171:
8165:
8163:
8157:
8156:
8154:
8153:
8148:
8143:
8138:
8132:
8130:
8121:
8115:
8114:
8111:
8110:
8108:
8107:
8102:
8097:
8092:
8087:
8081:
8079:
8073:
8072:
8070:
8069:
8064:
8059:
8051:
8046:
8041:
8040:
8039:
8037:partial (PACF)
8028:
8026:
8020:
8019:
8017:
8016:
8011:
8006:
7998:
7993:
7987:
7985:
7984:Specific tests
7981:
7980:
7978:
7977:
7972:
7967:
7962:
7957:
7952:
7947:
7942:
7936:
7934:
7927:
7921:
7920:
7918:
7917:
7916:
7915:
7914:
7913:
7898:
7897:
7896:
7886:
7884:Classification
7881:
7876:
7871:
7866:
7861:
7856:
7850:
7848:
7842:
7841:
7839:
7838:
7833:
7831:McNemar's test
7828:
7823:
7818:
7813:
7807:
7805:
7795:
7794:
7777:
7770:
7769:
7766:
7765:
7762:
7761:
7759:
7758:
7753:
7748:
7743:
7737:
7735:
7729:
7728:
7726:
7725:
7709:
7703:
7701:
7695:
7694:
7692:
7691:
7686:
7681:
7676:
7671:
7669:Semiparametric
7666:
7661:
7655:
7653:
7649:
7648:
7646:
7645:
7640:
7635:
7630:
7624:
7622:
7616:
7615:
7613:
7612:
7607:
7602:
7597:
7592:
7586:
7584:
7578:
7577:
7575:
7574:
7569:
7564:
7559:
7553:
7551:
7541:
7540:
7537:
7536:
7531:
7525:
7524:
7517:
7516:
7513:
7512:
7509:
7508:
7506:
7505:
7504:
7503:
7493:
7488:
7483:
7482:
7481:
7476:
7465:
7463:
7457:
7456:
7453:
7452:
7450:
7449:
7444:
7443:
7442:
7434:
7426:
7410:
7407:(MannâWhitney)
7402:
7401:
7400:
7387:
7386:
7385:
7374:
7372:
7366:
7365:
7363:
7362:
7361:
7360:
7355:
7350:
7340:
7335:
7332:(ShapiroâWilk)
7327:
7322:
7317:
7312:
7307:
7299:
7293:
7291:
7285:
7284:
7282:
7281:
7273:
7264:
7252:
7246:
7244:Specific tests
7240:
7239:
7236:
7235:
7233:
7232:
7227:
7222:
7216:
7214:
7208:
7207:
7205:
7204:
7199:
7198:
7197:
7187:
7186:
7185:
7175:
7169:
7167:
7161:
7160:
7158:
7157:
7156:
7155:
7150:
7140:
7135:
7130:
7125:
7120:
7114:
7112:
7106:
7105:
7103:
7102:
7097:
7096:
7095:
7090:
7089:
7088:
7083:
7068:
7067:
7066:
7061:
7056:
7051:
7040:
7038:
7029:
7023:
7022:
7020:
7019:
7014:
7009:
7008:
7007:
6997:
6992:
6991:
6990:
6980:
6979:
6978:
6973:
6968:
6958:
6953:
6948:
6947:
6946:
6941:
6936:
6920:
6919:
6918:
6913:
6908:
6898:
6897:
6896:
6891:
6881:
6880:
6879:
6869:
6868:
6867:
6857:
6852:
6847:
6841:
6839:
6829:
6828:
6823:
6816:
6815:
6812:
6811:
6808:
6807:
6805:
6804:
6799:
6794:
6789:
6783:
6781:
6775:
6774:
6772:
6771:
6766:
6761:
6755:
6753:
6749:
6748:
6746:
6745:
6740:
6735:
6730:
6725:
6720:
6715:
6709:
6707:
6701:
6700:
6698:
6697:
6695:Standard error
6692:
6687:
6682:
6681:
6680:
6675:
6664:
6662:
6656:
6655:
6653:
6652:
6647:
6642:
6637:
6632:
6627:
6625:Optimal design
6622:
6617:
6611:
6609:
6599:
6598:
6593:
6586:
6585:
6582:
6581:
6578:
6577:
6575:
6574:
6569:
6564:
6559:
6554:
6549:
6544:
6539:
6534:
6529:
6524:
6519:
6514:
6509:
6504:
6498:
6496:
6490:
6489:
6487:
6486:
6481:
6480:
6479:
6474:
6464:
6459:
6453:
6451:
6445:
6444:
6442:
6441:
6436:
6431:
6425:
6423:
6422:Summary tables
6419:
6418:
6416:
6415:
6409:
6407:
6401:
6400:
6397:
6396:
6394:
6393:
6392:
6391:
6386:
6381:
6371:
6365:
6363:
6357:
6356:
6354:
6353:
6348:
6343:
6338:
6333:
6328:
6323:
6317:
6315:
6309:
6308:
6306:
6305:
6300:
6295:
6294:
6293:
6288:
6283:
6278:
6273:
6268:
6263:
6258:
6256:Contraharmonic
6253:
6248:
6237:
6235:
6226:
6216:
6215:
6210:
6203:
6202:
6200:
6199:
6194:
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6169:
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6114:
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6096:
6091:
6083:
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6013:
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6007:
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5997:
5989:
5987:
5974:
5973:
5971:
5970:
5965:
5959:
5958:
5946:
5934:
5929:
5921:
5920:
5912:
5907:
5899:
5898:
5893:
5888:
5882:
5880:
5869:
5868:
5866:
5865:
5860:
5855:
5848:
5843:
5838:
5833:
5828:
5823:
5815:
5813:
5802:
5801:
5799:
5798:
5793:
5788:
5783:
5778:
5773:
5766:Optimal design
5761:
5760:
5755:
5750:
5738:
5733:
5728:
5722:
5720:
5712:
5711:
5706:
5704:
5703:
5696:
5689:
5681:
5675:
5674:
5645:Grime, James.
5642:
5631:
5624:
5615:
5614:at Convergence
5609:
5590:
5582:
5581:External links
5579:
5578:
5577:
5572:
5559:
5554:
5532:
5527:
5514:
5502:
5490:
5451:
5446:
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5380:
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5361:
5349:
5337:
5325:
5313:
5298:
5286:
5274:
5261:
5233:
5221:
5209:
5191:(4): 305â318,
5166:
5130:
5121:
5109:
5097:
5085:
5073:
5061:
5043:
5025:
4973:
4909:
4873:
4835:(5): 734â737,
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4697:
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4099:
4098:
4089:
4074:-sets (called
4065:
4056:-sets (called
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2755:Main article:
2752:
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2743:. There exist
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2196:
2192:
2184:
2180:
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2170:
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2129:
2126:
2041:Main article:
2038:
2035:
1995:) is called a
1967:
1966:
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1199:
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1021:
1019:
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1009:
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1004:
1002:
999:
997:
994:
993:
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987:
985:
982:
980:
977:
975:
972:
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968:
965:
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958:
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950:
949:
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937:
935:
932:
930:
927:
925:
922:
921:
918:
915:
913:
910:
908:
905:
903:
900:
899:
896:
893:
891:
888:
886:
883:
881:
878:
877:
874:
871:
869:
866:
864:
861:
859:
856:
855:
846:
843:
841:
838:
836:
833:
831:
828:
827:
824:
821:
819:
816:
814:
811:
809:
806:
805:
802:
799:
797:
794:
792:
789:
787:
784:
783:
780:
777:
775:
772:
770:
767:
765:
762:
761:
723:
720:
697:
694:
662:Remington Rand
646:Euler spoilers
585:
582:
578:Leonhard Euler
575:
558:St. Petersburg
545:
542:
535:
534:
480:
476:
475:
421:
417:
416:
413:
388:Martin Gardner
377:Jacques Ozanam
368:
365:
316:
313:
309:Greek alphabet
292:Latin alphabet
270: = {
263:Leonhard Euler
215:
214:
211:
204:
202:
199:
192:
190:
187:
180:
178:
70:
67:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
8498:
8487:
8486:Latin squares
8484:
8483:
8481:
8466:
8465:
8456:
8454:
8453:
8444:
8442:
8441:
8436:
8430:
8428:
8427:
8418:
8417:
8414:
8400:
8397:
8395:
8394:Geostatistics
8392:
8390:
8387:
8385:
8382:
8380:
8377:
8376:
8374:
8372:
8368:
8362:
8361:Psychometrics
8359:
8357:
8354:
8352:
8349:
8347:
8344:
8342:
8339:
8337:
8334:
8332:
8329:
8327:
8324:
8322:
8319:
8317:
8314:
8313:
8311:
8309:
8305:
8299:
8296:
8294:
8291:
8289:
8285:
8282:
8280:
8277:
8275:
8272:
8270:
8267:
8266:
8264:
8262:
8258:
8252:
8249:
8247:
8244:
8242:
8238:
8235:
8233:
8230:
8229:
8227:
8225:
8224:Biostatistics
8221:
8217:
8213:
8208:
8204:
8186:
8185:Log-rank test
8183:
8182:
8180:
8176:
8170:
8167:
8166:
8164:
8162:
8158:
8152:
8149:
8147:
8144:
8142:
8139:
8137:
8134:
8133:
8131:
8129:
8125:
8122:
8120:
8116:
8106:
8103:
8101:
8098:
8096:
8093:
8091:
8088:
8086:
8083:
8082:
8080:
8078:
8074:
8068:
8065:
8063:
8060:
8058:
8056:(BoxâJenkins)
8052:
8050:
8047:
8045:
8042:
8038:
8035:
8034:
8033:
8030:
8029:
8027:
8025:
8021:
8015:
8012:
8010:
8009:DurbinâWatson
8007:
8005:
7999:
7997:
7994:
7992:
7991:DickeyâFuller
7989:
7988:
7986:
7982:
7976:
7973:
7971:
7968:
7966:
7965:Cointegration
7963:
7961:
7958:
7956:
7953:
7951:
7948:
7946:
7943:
7941:
7940:Decomposition
7938:
7937:
7935:
7931:
7928:
7926:
7922:
7912:
7909:
7908:
7907:
7904:
7903:
7902:
7899:
7895:
7892:
7891:
7890:
7887:
7885:
7882:
7880:
7877:
7875:
7872:
7870:
7867:
7865:
7862:
7860:
7857:
7855:
7852:
7851:
7849:
7847:
7843:
7837:
7834:
7832:
7829:
7827:
7824:
7822:
7819:
7817:
7814:
7812:
7811:Cohen's kappa
7809:
7808:
7806:
7804:
7800:
7796:
7792:
7788:
7784:
7780:
7775:
7771:
7757:
7754:
7752:
7749:
7747:
7744:
7742:
7739:
7738:
7736:
7734:
7730:
7724:
7720:
7716:
7710:
7708:
7705:
7704:
7702:
7700:
7696:
7690:
7687:
7685:
7682:
7680:
7677:
7675:
7672:
7670:
7667:
7665:
7664:Nonparametric
7662:
7660:
7657:
7656:
7654:
7650:
7644:
7641:
7639:
7636:
7634:
7631:
7629:
7626:
7625:
7623:
7621:
7617:
7611:
7608:
7606:
7603:
7601:
7598:
7596:
7593:
7591:
7588:
7587:
7585:
7583:
7579:
7573:
7570:
7568:
7565:
7563:
7560:
7558:
7555:
7554:
7552:
7550:
7546:
7542:
7535:
7532:
7530:
7527:
7526:
7522:
7518:
7502:
7499:
7498:
7497:
7494:
7492:
7489:
7487:
7484:
7480:
7477:
7475:
7472:
7471:
7470:
7467:
7466:
7464:
7462:
7458:
7448:
7445:
7441:
7435:
7433:
7427:
7425:
7419:
7418:
7417:
7414:
7413:Nonparametric
7411:
7409:
7403:
7399:
7396:
7395:
7394:
7388:
7384:
7383:Sample median
7381:
7380:
7379:
7376:
7375:
7373:
7371:
7367:
7359:
7356:
7354:
7351:
7349:
7346:
7345:
7344:
7341:
7339:
7336:
7334:
7328:
7326:
7323:
7321:
7318:
7316:
7313:
7311:
7308:
7306:
7304:
7300:
7298:
7295:
7294:
7292:
7290:
7286:
7280:
7278:
7274:
7272:
7270:
7265:
7263:
7258:
7254:
7253:
7250:
7247:
7245:
7241:
7231:
7228:
7226:
7223:
7221:
7218:
7217:
7215:
7213:
7209:
7203:
7200:
7196:
7193:
7192:
7191:
7188:
7184:
7181:
7180:
7179:
7176:
7174:
7171:
7170:
7168:
7166:
7162:
7154:
7151:
7149:
7146:
7145:
7144:
7141:
7139:
7136:
7134:
7131:
7129:
7126:
7124:
7121:
7119:
7116:
7115:
7113:
7111:
7107:
7101:
7098:
7094:
7091:
7087:
7084:
7082:
7079:
7078:
7077:
7074:
7073:
7072:
7069:
7065:
7062:
7060:
7057:
7055:
7052:
7050:
7047:
7046:
7045:
7042:
7041:
7039:
7037:
7033:
7030:
7028:
7024:
7018:
7015:
7013:
7010:
7006:
7003:
7002:
7001:
6998:
6996:
6993:
6989:
6988:loss function
6986:
6985:
6984:
6981:
6977:
6974:
6972:
6969:
6967:
6964:
6963:
6962:
6959:
6957:
6954:
6952:
6949:
6945:
6942:
6940:
6937:
6935:
6929:
6926:
6925:
6924:
6921:
6917:
6914:
6912:
6909:
6907:
6904:
6903:
6902:
6899:
6895:
6892:
6890:
6887:
6886:
6885:
6882:
6878:
6875:
6874:
6873:
6870:
6866:
6863:
6862:
6861:
6858:
6856:
6853:
6851:
6848:
6846:
6843:
6842:
6840:
6838:
6834:
6830:
6826:
6821:
6817:
6803:
6800:
6798:
6795:
6793:
6790:
6788:
6785:
6784:
6782:
6780:
6776:
6770:
6767:
6765:
6762:
6760:
6757:
6756:
6754:
6750:
6744:
6741:
6739:
6736:
6734:
6731:
6729:
6726:
6724:
6721:
6719:
6716:
6714:
6711:
6710:
6708:
6706:
6702:
6696:
6693:
6691:
6690:Questionnaire
6688:
6686:
6683:
6679:
6676:
6674:
6671:
6670:
6669:
6666:
6665:
6663:
6661:
6657:
6651:
6648:
6646:
6643:
6641:
6638:
6636:
6633:
6631:
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6612:
6610:
6608:
6604:
6600:
6596:
6591:
6587:
6573:
6570:
6568:
6565:
6563:
6560:
6558:
6555:
6553:
6550:
6548:
6545:
6543:
6540:
6538:
6535:
6533:
6530:
6528:
6525:
6523:
6520:
6518:
6517:Control chart
6515:
6513:
6510:
6508:
6505:
6503:
6500:
6499:
6497:
6495:
6491:
6485:
6482:
6478:
6475:
6473:
6470:
6469:
6468:
6465:
6463:
6460:
6458:
6455:
6454:
6452:
6450:
6446:
6440:
6437:
6435:
6432:
6430:
6427:
6426:
6424:
6420:
6414:
6411:
6410:
6408:
6406:
6402:
6390:
6387:
6385:
6382:
6380:
6377:
6376:
6375:
6372:
6370:
6367:
6366:
6364:
6362:
6358:
6352:
6349:
6347:
6344:
6342:
6339:
6337:
6334:
6332:
6329:
6327:
6324:
6322:
6319:
6318:
6316:
6314:
6310:
6304:
6301:
6299:
6296:
6292:
6289:
6287:
6284:
6282:
6279:
6277:
6274:
6272:
6269:
6267:
6264:
6262:
6259:
6257:
6254:
6252:
6249:
6247:
6244:
6243:
6242:
6239:
6238:
6236:
6234:
6230:
6227:
6225:
6221:
6217:
6213:
6208:
6204:
6198:
6195:
6193:
6190:
6189:
6186:
6182:
6175:
6170:
6168:
6163:
6161:
6156:
6155:
6152:
6140:
6137:
6135:
6132:
6130:
6125:
6120:
6118:
6115:
6113:
6110:
6109:
6106:
6100:
6097:
6095:
6092:
6090:
6089:
6085:
6084:
6081:
6078:
6076:
6075:
6070:
6067:
6065:
6062:
6060:
6057:
6055:
6052:
6049:
6046:
6044:
6043:
6039:
6038:
6035:
6032:
6030:
6027:
6025:
6022:
6020:
6019:
6015:
6014:
6011:
6008:
6006:
6003:
6001:
5998:
5996:
5995:
5991:
5990:
5988:
5986:
5979:
5975:
5969:
5966:
5964:
5963:Compare means
5961:
5960:
5957:
5955:
5951:
5947:
5945:
5943:
5939:
5935:
5933:
5930:
5928:
5927:
5923:
5922:
5919:
5916:
5913:
5911:
5908:
5906:
5905:
5904:Random effect
5901:
5900:
5897:
5894:
5892:
5889:
5887:
5884:
5883:
5881:
5879:
5874:
5870:
5864:
5861:
5859:
5856:
5854:
5853:
5849:
5847:
5846:Orthogonality
5844:
5842:
5839:
5837:
5834:
5832:
5829:
5827:
5824:
5822:
5821:
5817:
5816:
5814:
5812:
5807:
5803:
5797:
5794:
5792:
5789:
5787:
5784:
5782:
5781:Randomization
5779:
5777:
5774:
5772:
5768:
5767:
5763:
5762:
5759:
5756:
5754:
5751:
5749:
5746:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5724:
5723:
5721:
5719:
5713:
5709:
5702:
5697:
5695:
5690:
5688:
5683:
5682:
5679:
5663:
5659:
5655:
5648:
5643:
5640:
5636:
5632:
5630:
5629:
5625:
5623:
5619:
5616:
5613:
5610:
5605:
5604:
5599:
5596:
5591:
5588:
5585:
5584:
5580:
5575:
5569:
5565:
5560:
5557:
5555:0-19-853256-3
5551:
5547:
5546:
5541:
5537:
5533:
5530:
5524:
5520:
5515:
5511:
5507:
5503:
5499:
5495:
5491:
5487:
5483:
5479:
5475:
5472:(2): 98â119,
5471:
5467:
5460:
5456:
5452:
5449:
5447:0-671-20913-2
5443:
5439:
5435:
5431:
5428:
5424:
5420:
5418:0-12-209350-X
5414:
5410:
5405:
5402:
5396:
5391:
5390:
5383:
5382:
5378:
5370:
5365:
5362:
5358:
5353:
5350:
5346:
5341:
5338:
5334:
5329:
5326:
5322:
5317:
5314:
5310:
5305:
5303:
5299:
5295:
5290:
5287:
5283:
5278:
5275:
5264:
5262:9780521772310
5258:
5254:
5250:
5246:
5245:
5237:
5234:
5230:
5225:
5222:
5218:
5213:
5210:
5206:
5202:
5198:
5194:
5190:
5186:
5185:
5180:
5176:
5175:Lam, C. W. H.
5170:
5167:
5163:
5159:
5154:
5149:
5145:
5141:
5134:
5131:
5125:
5122:
5118:
5113:
5110:
5106:
5101:
5098:
5094:
5089:
5086:
5082:
5077:
5074:
5070:
5065:
5062:
5058:
5054:
5047:
5044:
5040:
5036:
5029:
5026:
5022:
5018:
5014:
5010:
5006:
5002:
4997:
4992:
4989:(6): 062326,
4988:
4984:
4977:
4974:
4970:
4966:
4962:
4958:
4954:
4950:
4946:
4942:
4937:
4932:
4929:(8): 080507,
4928:
4924:
4916:
4914:
4910:
4906:
4902:
4897:
4892:
4888:
4884:
4877:
4874:
4870:
4866:
4861:
4856:
4851:
4846:
4842:
4838:
4834:
4830:
4826:
4819:
4816:
4812:
4807:
4804:
4799:
4795:
4788:
4785:
4780:
4776:
4769:
4766:
4762:
4757:
4755:
4753:
4751:
4749:
4747:
4743:
4740:
4736:
4732:
4731:
4724:
4721:
4716:
4712:
4708:
4701:
4698:
4694:
4689:
4686:
4683:, pp. 162-172
4682:
4677:
4675:
4671:
4668:
4662:
4661:
4653:
4650:
4647:
4643:
4637:
4633:
4632:
4624:
4621:
4618:, p. 156
4617:
4612:
4609:
4605:
4600:
4598:
4596:
4592:
4588:
4584:
4580:
4579:1-permutation
4576:
4572:
4566:
4563:
4556:
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4532:
4527:
4525:
4523:
4519:
4518:Georges Perec
4515:
4514:magic squares
4511:
4507:
4503:
4495:
4493:
4487:
4482:
4478:
4473:
4453:
4444:
4443:
4439:
4438:
4434:
4433:
4429:
4428:
4424:
4423:
4420:
4419:
4418:
4408:
4399:
4397:9 11 18 3 10
4396:
4387:
4385:9 12 16 2 15
4384:
4375:
4373:9 14 19 1 20
4372:
4363:
4362:
4359:8 14 16 4 10
4358:
4349:
4346:
4337:
4335:8 11 17 2 20
4334:
4325:
4323:8 13 18 1 15
4322:
4313:
4312:
4309:7 11 19 4 15
4308:
4299:
4297:7 13 16 3 20
4296:
4287:
4284:
4275:
4273:7 12 17 1 10
4272:
4263:
4262:
4259:6 12 18 4 20
4258:
4249:
4247:6 14 17 3 15
4246:
4237:
4235:6 13 19 2 10
4234:
4225:
4222:
4213:
4212:
4209:
4208:
4207:
4196:
4183:
4170:
4161:
4148:
4118:
4115:
4110:
4077:
4066:
4059:
4049:
4045:
4038:
4031:
4027:
4023:
4013:
4012:
4011:
3997:
3989:
3980:
3971:
3968:
3959:
3956:
3947:
3944:
3935:
3934:
3930:
3921:
3918:
3909:
3906:
3897:
3894:
3885:
3884:
3880:
3871:
3868:
3859:
3856:
3847:
3844:
3835:
3834:
3830:
3821:
3818:
3809:
3806:
3797:
3794:
3785:
3784:
3780:
3771:
3768:
3759:
3756:
3747:
3744:
3735:
3734:
3731:
3730:
3729:
3726:
3715:
3706:
3685:
3679:
3675:
3670:
3666:
3661:
3640:
3611:
3592:
3577:
3564:each of size
3563:
3559:
3552:and a set of
3551:
3535:
3533:
3530:
3528:
3524:
3508:
3504:
3500:
3496:
3484:
3481:
3478:
3475:
3472:
3471:
3467:
3464:
3461:
3458:
3455:
3454:
3450:
3447:
3444:
3441:
3438:
3437:
3433:
3430:
3427:
3424:
3421:
3420:
3416:
3413:
3410:
3407:
3404:
3403:
3399:
3396:
3393:
3390:
3387:
3386:
3382:
3379:
3376:
3373:
3370:
3369:
3365:
3362:
3359:
3356:
3353:
3352:
3348:
3345:
3342:
3339:
3336:
3335:
3331:
3328:
3325:
3322:
3319:
3318:
3314:
3311:
3308:
3305:
3302:
3301:
3297:
3294:
3291:
3288:
3285:
3284:
3280:
3277:
3274:
3271:
3268:
3267:
3263:
3260:
3257:
3254:
3251:
3250:
3246:
3243:
3240:
3237:
3234:
3233:
3229:
3226:
3223:
3220:
3217:
3216:
3209:
3203:
3197:
3194:
3191:
3190:
3187:
3186:
3185:
3160:
3156:
3147:
3142:
3137:
3132:
3125:
3120:
3115:
3110:
3103:
3098:
3093:
3088:
3081:
3076:
3071:
3066:
3049:
3045:
3036:
3031:
3026:
3021:
3014:
3009:
3004:
2999:
2992:
2987:
2982:
2977:
2970:
2965:
2960:
2955:
2938:
2934:
2925:
2920:
2915:
2910:
2903:
2898:
2893:
2888:
2881:
2876:
2871:
2866:
2859:
2854:
2849:
2844:
2833:
2832:
2831:
2812:
2810:
2802:
2777:
2773:
2764:
2758:
2750:
2748:
2746:
2742:
2737:
2731:
2723:
2685:
2666:
2557:
2556:
2555:
2554:
2553:
2547:
2539:
2531:
2519:
2516:
2500:
2498:
2495:
2489:
2483:
2477:
2457:
2453:
2442:
2436:
2425:
2423:
2418:
2412:
2406:
2374:
2368:
2365:
2358:
2354:
2348:
2344:
2335:
2332:
2327:
2314:
2313:
2312:
2311:
2310:
2294:
2290:
2286:
2283:
2280:
2275:
2271:
2267:
2262:
2258:
2229:
2225:
2219:
2215:
2211:
2204:
2200:
2194:
2190:
2182:
2178:
2172:
2168:
2164:
2161:
2153:
2149:
2146:
2140:
2125:
2122:
2093:
2088:
2076:
2074:
2070:
2065:
2060:
2051:
2044:
2036:
2034:
2032:
2031:combinatorics
2027:
2021:
2016:
2012:
2008:
2003:
1998:
1974:
1972:
1971:standard form
1964:
1961:
1958:
1957:
1956:
1950:
1948:
1946:
1938:
1934:
1930:
1926:
1922:
1918:
1916:
1915:
1910:
1909:
1904:
1903:
1898:
1897:
1892:
1891:
1886:
1884:
1880:
1876:
1872:
1868:
1864:
1862:
1858:
1854:
1850:
1846:
1842:
1841:
1840:
1819:
1802:
1785:
1768:
1751:
1745:
1741:
1739:
1727:
1724:
1721:
1718:
1715:
1714:
1710:
1707:
1704:
1701:
1698:
1697:
1693:
1690:
1687:
1684:
1681:
1680:
1676:
1673:
1670:
1667:
1664:
1663:
1659:
1656:
1653:
1650:
1647:
1646:
1643:
1642:
1641:
1624:
1617:
1612:
1607:
1602:
1597:
1590:
1585:
1580:
1575:
1570:
1563:
1558:
1553:
1548:
1543:
1536:
1531:
1526:
1521:
1516:
1509:
1504:
1499:
1494:
1489:
1477:
1472:
1467:
1462:
1457:
1450:
1445:
1440:
1435:
1430:
1423:
1418:
1413:
1408:
1403:
1396:
1391:
1386:
1381:
1376:
1369:
1364:
1359:
1354:
1349:
1337:
1332:
1327:
1322:
1317:
1310:
1305:
1300:
1295:
1290:
1283:
1278:
1273:
1268:
1263:
1256:
1251:
1246:
1241:
1236:
1229:
1224:
1219:
1214:
1209:
1197:
1192:
1187:
1182:
1177:
1170:
1165:
1160:
1155:
1150:
1143:
1138:
1133:
1128:
1123:
1116:
1111:
1106:
1101:
1096:
1089:
1084:
1079:
1074:
1069:
1058:
1057:
1056:
1039:
1032:
1027:
1022:
1017:
1010:
1005:
1000:
995:
988:
983:
978:
973:
966:
961:
956:
951:
938:
933:
928:
923:
916:
911:
906:
901:
894:
889:
884:
879:
872:
867:
862:
857:
844:
839:
834:
829:
822:
817:
812:
807:
800:
795:
790:
785:
778:
773:
768:
763:
752:
751:
750:
747:
745:
743:
737:
733:
729:
721:
719:
717:
713:
702:
695:
693:
689:
682:
675:
669:
667:
663:
659:
655:
651:
647:
643:
639:
634:
632:
631:combinatorics
628:
624:
618:
614:
609:
604:
595:
590:
574:
569:
567:
563:
559:
550:
543:
541:
478:
477:
419:
418:
410:
407:
405:
401:
397:
393:
389:
386:According to
384:
381:
378:
374:
373:playing cards
366:
364:
353:
350:
348:
343:
341:
337:
332:
329:
326:
322:
314:
312:
310:
305:
301:}, the first
298:
293:
288:
284:}, the first
281:
277:
273:
269:
264:
259:
256:
252:
248:
242:
238:
232:
227:
221:
208:
203:
196:
191:
184:
179:
176:
174:
171:
165:
159:
153:
147:
141:
134:
130:
125:
120:
116:
110:
104:
98:
94:
89:
84:
80:
76:
68:
66:
64:
59:
57:
53:
49:
45:
41:
37:
36:Latin squares
33:
19:
8462:
8450:
8431:
8424:
8336:Econometrics
8286: /
8269:Chemometrics
8246:Epidemiology
8239: /
8212:Applications
8054:ARIMA model
8001:Q-statistic
7950:Stationarity
7846:Multivariate
7789: /
7785: /
7783:Multivariate
7781: /
7721: /
7717: /
7491:Bayes factor
7390:Signed rank
7302:
7276:
7268:
7256:
6951:Completeness
6787:Cohort study
6685:Opinion poll
6620:Missing data
6607:Study design
6562:Scatter plot
6484:Scatter plot
6477:Spearman's Ï
6439:Grouped data
6086:
6072:
6054:Latin square
6040:
6016:
5992:
5953:
5949:
5942:multivariate
5941:
5937:
5924:
5902:
5850:
5818:
5764:
5666:. Retrieved
5653:
5637:and related
5627:
5622:cut-the-knot
5601:
5563:
5544:
5521:, Springer,
5518:
5509:
5497:
5469:
5465:
5440:, Fireside,
5437:
5408:
5388:
5364:
5352:
5340:
5328:
5316:
5309:Stinson 2004
5289:
5277:
5266:. Retrieved
5243:
5236:
5224:
5212:
5188:
5182:
5169:
5143:
5139:
5133:
5124:
5112:
5100:
5088:
5076:
5064:
5056:
5046:
5038:
5028:
4986:
4982:
4976:
4926:
4922:
4886:
4882:
4876:
4832:
4828:
4824:
4818:
4806:
4797:
4793:
4787:
4778:
4774:
4768:
4729:
4723:
4714:
4710:
4700:
4688:
4681:Gardner 1966
4659:
4652:
4630:
4623:
4611:
4582:
4578:
4574:
4570:
4565:
4540:Block design
4499:
4496:Applications
4480:
4476:
4457:
4454:Graph theory
4435:16 17 18 19
4430:11 12 13 14
4416:
4409:9 13 17 4 5
4347:8 12 19 3 5
4285:7 14 18 2 5
4223:6 11 16 1 5
4194:
4181:
4168:
4159:
4149:
4111:
4100:
4075:
4057:
4047:
4043:
4036:
4029:
4025:
4017:is a set of
3995:
3993:
3727:
3713:
3704:
3683:
3677:
3673:
3668:
3664:
3659:
3612:
3593:
3578:
3561:
3557:
3549:
3539:
3531:
3526:
3522:
3506:
3502:
3498:
3494:
3492:
3183:
2813:
2808:
2800:
2775:
2771:
2762:
2760:
2738:
2729:
2721:
2664:
2586:
2545:
2544:elements of
2538:cyclic group
2529:
2517:
2515:finite field
2504:
2493:
2487:
2481:
2475:
2440:
2437:
2426:
2410:
2407:
2392:
2151:
2150:
2144:
2138:
2131:
2123:
2089:
2077:
2063:
2059:affine plane
2049:
2046:
2025:
2019:
2007:prime number
2001:
1996:
1975:
1970:
1968:
1954:
1942:
1912:
1906:
1900:
1894:
1888:
1838:
1742:
1735:
1639:
1054:
748:
741:
739:
735:
731:
727:
725:
708:
687:
680:
673:
670:
660:division of
650:E. T. Parker
645:
635:
623:Gaston Tarry
612:
602:
599:
571:
565:
555:
538:
479:Solution #2
420:Solution #1
415:Normal form
385:
382:
370:
354:
351:
346:
344:
336:Cayley table
333:
330:
324:
320:
318:
303:
296:
286:
279:
275:
271:
267:
260:
254:
250:
240:
236:
231:Latin square
225:
219:
216:
169:
163:
157:
151:
145:
139:
132:
128:
124:ordered pair
118:
114:
108:
102:
96:
87:
82:
79:Euler square
78:
74:
72:
62:
60:
47:
43:
39:
29:
8464:WikiProject
8379:Cartography
8341:Jurimetrics
8293:Reliability
8024:Time domain
8003:(LjungâBox)
7925:Time-series
7803:Categorical
7787:Time-series
7779:Categorical
7714:(Bernoulli)
7549:Correlation
7529:Correlation
7325:JarqueâBera
7297:Chi-squared
7059:M-estimator
7012:Asymptotics
6956:Sufficiency
6723:Interaction
6635:Replication
6615:Effect size
6572:Violin plot
6552:Radar chart
6532:Forest plot
6522:Correlogram
6472:Kendall's Ï
6029:BoxâBehnken
5910:Mixed model
5841:Confounding
5836:Interaction
5826:Effect size
5796:Sample size
5658:Brady Haran
5639:source code
5057:LiveScience
4889:: 189â203,
4445:5 10 15 20
4127:points and
3621:)-net from
2574:= λ, ..., α
2142:except for
2103:⥠1 (mod 4)
2098:exists and
2082:) exist if
654:UNIVAC 1206
347:group based
325:transversal
81:or pair of
8331:Demography
8049:ARMA model
7854:Regression
7431:(Friedman)
7392:(Wilcoxon)
7330:Normality
7320:Lilliefors
7267:Student's
7143:Resampling
7017:Robustness
7005:divergence
6995:Efficiency
6933:(monotone)
6928:Likelihood
6845:Population
6678:Stratified
6630:Population
6449:Dependence
6405:Count data
6336:Percentile
6313:Dispersion
6246:Arithmetic
6181:Statistics
5985:randomized
5983:Completely
5954:covariance
5716:Scientific
5379:References
5268:2019-07-06
4996:1708.05946
4936:2104.05122
4645:. Errata:
4468:complete (
4021:varieties;
3687:column is
1937:slab-serif
1929:monospaced
1925:sans-serif
1887:the text:
712:ƻyczkowski
625:through a
608:oddly even
396:Rouse Ball
282:, ...
44:orthogonal
7712:Logistic
7479:posterior
7405:Rank sum
7153:Jackknife
7148:Bootstrap
6966:Bootstrap
6901:Parameter
6850:Statistic
6645:Statistic
6557:Run chart
6542:Pie chart
6537:Histogram
6527:Fan chart
6502:Bar chart
6384:L-moments
6271:Geometric
5994:Factorial
5878:inference
5858:Covariate
5820:Treatment
5806:Treatment
5603:MathWorld
5162:123440808
5146:: 88â93,
4969:236950798
4575:directrix
4573:(Euler),
4488:of order
4458:A set of
4010:) where:
3594:A set of
2635:â 0) is L
2497:> 90.
2366:−
2355:α
2328:≥
2284:⋯
2226:α
2212:⋯
2201:α
2179:α
2061:of order
2053:â 1 MOLS(
2047:A set of
1985:− 1
638:R.C. Bose
636:In 1959,
412:Solution
315:Existence
245:from the
91:over two
85:of order
8480:Category
8426:Category
8119:Survival
7996:Johansen
7719:Binomial
7674:Isotonic
7261:(normal)
6906:location
6713:Blocking
6668:Sampling
6547:QâQ plot
6512:Box plot
6494:Graphics
6389:Skewness
6379:Kurtosis
6351:Variance
6281:Heronian
6276:Harmonic
6117:Category
6112:Glossary
5918:Bayesian
5896:Bayesian
5852:Blocking
5831:Contrast
5811:blocking
5771:Bayesian
5758:Blinding
5748:validity
5745:external
5741:Internal
5662:Archived
5542:(1987),
5496:(1988),
5436:(1966),
5359:, p. 135
5347:, p. 133
5335:, p. 270
5323:, p. 161
5311:, p. 140
5296:, p. 169
5284:, p. 167
5231:, p. 102
5219:, p. 390
5177:(1991),
5119:, p. 158
5107:, p. 159
5083:, p. 163
5071:, p. 160
5021:51532085
4961:35275648
4869:16590435
4763:, p. 162
4717:: 50â63.
4606:, p. 155
4589:, p. 29)
4583:diagonal
4528:See also
4440:1 2 3 4
4425:6 7 8 9
4105:-2 MOLS(
4082:-set in
2801:strength
2787:â„ 2 and
2708:â 0 and
2704:, where
2617:-1 (mod
2605:, where
1728:4,3,1,2
1725:3,2,5,1
1722:2,1,4,5
1719:1,5,3,4
1716:5,4,2,3
1711:3,1,2,4
1708:2,5,1,3
1705:1,4,5,2
1702:5,3,4,1
1699:4,2,3,5
1694:2,4,3,1
1691:1,3,2,5
1688:5,2,1,4
1685:4,1,5,3
1682:3,5,4,2
1677:1,2,4,3
1674:5,1,3,2
1671:4,5,2,1
1668:3,4,1,5
1665:2,3,5,4
1660:5,5,5,5
1657:4,4,4,4
1654:3,3,3,3
1651:2,2,2,2
1648:1,1,1,1
576:â
137:, where
8452:Commons
8399:Kriging
8284:Process
8241:studies
8100:Wavelet
7933:General
7100:Plug-in
6894:L space
6673:Cluster
6374:Moments
6192:Outline
6010:Taguchi
5978:Designs
5736:Control
5654:YouTube
5650:(video)
5427:0351850
5371:, p.257
5205:2323798
5095:, p. 98
5001:Bibcode
4941:Bibcode
4905:0122729
4837:Bibcode
4813:, p.267
4727:Euler:
4695:, p.251
4667:Fig. 35
4535:36 cube
4119:of an (
4042:, ...,
4008:X, G, B
3637:) (see
3610:)-net.
3576:lines.
3517:) with
2536:) is a
2420:in the
2417:A001438
1933:cursive
1833:fjords
1830:zincky
1827:qiviut
1824:phlegm
1821:jawbox
1816:jawbox
1813:fjords
1810:zincky
1807:qiviut
1804:phlegm
1799:phlegm
1796:jawbox
1793:fjords
1790:zincky
1787:qiviut
1782:qiviut
1779:phlegm
1776:jawbox
1773:fjords
1770:zincky
1765:zincky
1762:qiviut
1759:phlegm
1756:jawbox
1753:fjords
705:states.
690:= 2, 6.
685:except
610:number
367:History
278:,
274:,
253:×
239:,
212:Order 5
200:Order 4
188:Order 3
117:×
8321:Census
7911:Normal
7859:Manova
7679:Robust
7429:2-way
7421:1-way
7259:-test
6930:
6507:Biplot
6298:Median
6291:Lehmer
6233:Center
6050:(GRBD)
5950:Ancova
5938:Manova
5873:Models
5718:method
5570:
5552:
5525:
5484:
5444:
5425:
5415:
5397:
5259:
5203:
5160:
5019:
4967:
4959:
4903:
4867:
4860:222625
4857:
4638:
4581:, and
4508:, and
4189:, and
4076:blocks
4058:groups
3562:blocks
3550:points
2814:An OA(
2779:array
2631:(with
2570:= λ, α
2566:= 1, α
2562:= 0, α
2309:then
1935:, and
1914:zincky
1911:, and
1908:qiviut
1902:phlegm
1896:jawbox
1890:fjords
1883:yellow
1881:, and
1861:silver
1859:, and
1849:maroon
658:UNIVAC
294:, and
155:is in
143:is in
34:, two
7945:Trend
7474:prior
7416:anova
7305:-test
7279:-test
7271:-test
7178:Power
7123:Pivot
6916:shape
6911:scale
6361:Shape
6341:Range
6286:Heinz
6261:Cubic
6197:Index
6042:Block
5668:9 May
5486:82321
5482:S2CID
5462:(PDF)
5201:JSTOR
5158:S2CID
5017:S2CID
4991:arXiv
4965:S2CID
4931:arXiv
4557:Notes
4492:+ 2.
4484:into
4479:,...,
4462:MOLS(
3998:with
3639:above
3633:+ 2,
3625:MOLS(
3617:+ 2,
3606:+ 2,
3598:MOLS(
3583:+ 1,
3558:lines
2826:MOLS(
2818:+ 2,
2809:index
2765:, OA(
2645:) = α
2154:: If
2067:(see
2011:power
2005:is a
1921:serif
1867:white
1845:black
1738:below
740:MOLS(
615:⥠2 (
340:group
40:order
8178:Test
7378:Sign
7230:Wald
6303:Mode
6241:Mean
5876:and
5809:and
5743:and
5670:2020
5568:ISBN
5550:ISBN
5523:ISBN
5442:ISBN
5413:ISBN
5395:ISBN
5257:ISBN
4957:PMID
4865:PMID
4715:XVII
4636:ISBN
4152:i, j
4114:dual
3708:and
3695:and
3645:and
3579:An (
3536:Nets
3525:and
3505:and
3497:and
2716:and
2696:) =
2623:i, j
2581:= λ.
2458:14.8
2422:OEIS
2069:Nets
1879:blue
1875:lime
1857:navy
1853:teal
736:MOLS
730:(or
676:â„ 7.
640:and
334:The
149:and
100:and
93:sets
7358:BIC
7353:AIC
5620:at
5474:doi
5249:doi
5193:doi
5148:doi
5009:doi
4949:doi
4927:128
4891:doi
4855:PMC
4845:doi
4198:â 5
4185:â 5
4121:k,n
4109:).
4054:k n
4028:= {
3560:or
3542:k,n
2811:).
2767:k,n
2761:An
2694:i,j
2651:+ α
2643:i,j
2599:= α
2424:).
2333:min
2105:or
2009:or
1871:red
1740:).
738:or
668:).
619:4).
617:mod
363:).
77:or
30:In
8482::
5769::
5660:.
5656:.
5652:.
5600:.
5538:;
5480:,
5470:15
5468:,
5464:,
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5255:.
5199:,
5189:98
5187:,
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5055:,
5037:,
5015:,
5007:,
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4987:97
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4963:,
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4901:MR
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4887:12
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4853:,
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4796:.
4777:.
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4713:.
4709:.
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4594:^
4577:,
4504:,
4406::
4404:41
4394::
4392:32
4382::
4380:23
4370::
4368:14
4356::
4354:42
4344::
4342:31
4332::
4330:24
4320::
4318:13
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4304:43
4294::
4292:34
4282::
4280:21
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4254:44
4244::
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4230:22
4220::
4218:11
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3994:A
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3876:34
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3852:32
3842::
3840:31
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3826:24
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3814:23
3804::
3802:22
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3790:21
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3192:r
2774:Ă
2730:GF
2722:GF
2712:,
2702:rj
2700:+
2675:=
2665:GF
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2579:-1
2546:GF
2530:GF
2518:GF
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2033:.
1931:,
1927:,
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633:.
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528:AâŁ
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518:Qâ
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3566:n
3546:n
3527:c
3523:r
3519:s
3515:n
3513:,
3511:s
3507:c
3503:r
3499:c
3495:r
3212:3
3210:L
3206:2
3204:L
3200:1
3198:L
3161:3
3157:L
3148:3
3143:4
3138:1
3133:2
3126:1
3121:2
3116:3
3111:4
3104:2
3099:1
3094:4
3089:3
3082:4
3077:3
3072:2
3067:1
3050:2
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3037:2
3032:1
3027:4
3022:3
3015:3
3010:4
3005:1
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2993:1
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2983:3
2978:4
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2921:2
2916:3
2911:4
2904:2
2899:1
2894:4
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2867:2
2860:4
2855:3
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2845:1
2828:n
2824:s
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2805:A
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2797:A
2793:n
2789:n
2785:k
2783:(
2781:A
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2734:p
2732:(
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2669:q
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2375:.
2372:}
2369:1
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2341:{
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2281:,
2276:2
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2268:,
2263:1
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2248:n
2230:r
2220:r
2216:p
2205:2
2195:2
2191:p
2183:1
2173:1
2169:p
2165:=
2162:n
2145:n
2139:n
2134:n
2119:n
2115:n
2111:n
2107:n
2101:n
2096:n
2084:n
2080:n
2064:n
2055:n
2050:n
2026:n
2020:n
2002:n
1993:n
1989:n
1983:n
1978:n
1939:.
1625:.
1618:2
1613:1
1608:5
1603:4
1598:3
1591:4
1586:3
1581:2
1576:1
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1564:1
1559:5
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1549:3
1544:2
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1532:2
1527:1
1522:5
1517:4
1510:5
1505:4
1500:3
1495:2
1490:1
1478:1
1473:5
1468:4
1463:3
1458:2
1451:2
1446:1
1441:5
1436:4
1431:3
1424:3
1419:2
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1397:4
1392:3
1387:2
1382:1
1377:5
1370:5
1365:4
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1355:2
1350:1
1338:3
1333:2
1328:1
1323:5
1318:4
1311:1
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1301:4
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1291:2
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1198:4
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1188:2
1183:1
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1161:1
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1151:4
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1134:5
1129:4
1124:3
1117:1
1112:5
1107:4
1102:3
1097:2
1090:5
1085:4
1080:3
1075:2
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1040:.
1033:3
1028:4
1023:1
1018:2
1011:1
1006:2
1001:3
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989:2
984:1
979:4
974:3
967:4
962:3
957:2
952:1
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924:3
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912:4
907:1
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818:1
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796:4
791:1
786:2
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764:1
744:)
742:n
688:n
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674:n
613:n
603:n
361:k
357:k
304:n
297:T
287:n
280:C
276:B
272:A
268:S
255:T
251:S
243:)
241:t
237:s
235:(
226:t
220:s
170:T
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158:T
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140:s
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133:t
129:s
127:(
119:n
115:n
109:n
103:T
97:S
88:n
20:)
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